# Digital matriculation exam in Finland

Lauri Hellsten (      laurihellsten, lauri.k.hellsten@gmail.com)

Espoon yhteislyseo Upper secondary school

University of Helsinki

What have we learned?

CC BY SA naosuke ii

# What guides the teacher?

CC BY SA naosuke ii

# What's going on?

• Focus on assessments for learning.
• Student must show diverse knowledge on the contents and goals of a course for the course assesment.
• Specific ICT skills as goals in STEM-courses.

Digital matriculation exam (math 2019, chemistry & physics 2018)

• Use of programs (GeoGebra, LoggerPro, etc.) in STEM-courses.
• New types of problems involving a large scale of different types of digital materials (real life data, videos, simulations, etc.) that couldn't be done in a paper exam.

# Digital matriculation exam

The digital matriculation exam in math has been held one time to this day.

# The digital exam system (abitti.fi)

Server

Router

Students laptop, booted from an USB-stick

Name Name
Dia Texas Instruments TI-Nspire CAS*
GeoGebra 5* ja 6* SpeedCrunch
GIMP Pinta
GNOME- Okular
Inkscape MarvinSketch
LibreOffice LoggerPro*
MAOL formula tables

# All programs in the Abitti system

1. Multiple choice and ordering problems containing minimal or no mathematical notation.

2. Problems that require small amount of mathematical notation and basic understanding from the courses.

3. Problems that require versatile knowledge and skills of mathematics from different courses and also problem solving skills.

Some of the problems of type 1 and 2 are to be done without CAS-calculators or spreadsheet programs.

# Digital matriculation exam in mathematics

Student can participate in the A-level (10+3 courses) or B-level (6+2 courses) math exam. The structure of the exam is the same in both level exams.

Part Problems to choose from Student answers max. points
A 4 4 48
B1 5 3 36
B2 4 3 36

120 p

### Background: Teaching problem solving skills and measuring them

” The matriculation exam has to measure knowledge, skills and maturity according to the curriculum. Not the skill in solving textbook problems." (translated)

Peter Hästö, head of mathematics in the matriculation exam board. kalvot

“ You can not practice or measure problem solving with problems you are familiar with! New problem types is the goal! ... The goal is to make as much of different type of problems that one is unable to remember or learn them all. "(translated)

"If it is in my hands, in the future we will see more 'nonstandard' problems where one has to apply the knowledge rather than produce routine solutions. ...
There was criticism about the problem in the B-level math  (2012) where one has to find the zero point of the function $$f(x)=\dfrac{x+3}{x^2-4}$$. The criticism was about these types of problems aren't taught in the B-level math."

Peter Hästö, head of mathematics in the matriculation exam board. Dimensio 4/2013.

"I think this problem is good because students don't practice these types of problems in the classroom. In the problem you need to apply information you know in a slightly different context, ..." (translated)

# Basic principle regarding answers done using programs

$$\longrightarrow$$ a software can be used to formulate any claim, but not to justify the truthfulness of it.

# Tools for answering in part A

SpeedCrunch and KCalc and Gnome

# Tools for answering in part B1 and B2

Everything in part A and

• LibreOffice Calc
• wxMaxima
• Texas Instruments TI-Nspire CAS
• Logger Pro
• GeoGebra 5 and 6
• 4f Vihko (finnish program)

# Tools for answering in part B1 and B2

Text

$$(5,2)$$

Let the circumference of a triangle be p and the area of it A. Let there be an another triangle that is equilatelar and its circumference also be p and its area B. Show that A $$\leq$$ B.

# Matriculation exam board: How to succeed in the digital mathematics exam?

https://www.ylioppilastutkinto.fi/ma (finnish and swedish)

# Thank you!

http://bit.ly/matrexam

My email lauri.k.hellsten@gmail.com

By Opetus.tv

• 727